Space of modular forms of level 1152, weight 4, and Character 1152.f

• Label: 1152.4.f
• Level: $1152$
• Weight: $4$
• Character orbit: 1152.f
• Rep. character: $\chi_{1152}(575,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $7$
• Sturm bound: $768$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1152.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(768\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1152, [\chi])\).

	Total	New	Old
Modular forms	608	48	560
Cusp forms	544	48	496
Eisenstein series	64	0	64

Trace form

\( 48 q + 1200 q^{25} - 5232 q^{49} + 1728 q^{73} - 12288 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1152.4.f.a	$1152$	$4$	1152.f	24.f	$2$	$4$	$4$	$67.970$	\(\Q(\zeta_{8})\)	None		✓			1152.4.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta_{2} q^{5}+4\beta_1 q^{7}+8\beta_{3} q^{11}+\cdots\)
1152.4.f.b	$1152$	$4$	1152.f	24.f	$2$	$4$	$4$	$67.970$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1152.4.f.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_{3} q^{5}+\beta_1 q^{13}+5\beta_{2} q^{17}+37 q^{25}+\cdots\)
1152.4.f.c	$1152$	$4$	1152.f	24.f	$2$	$4$	$4$	$67.970$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		✓			1152.4.f.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-13\beta_{2} q^{5}+\beta_1 q^{13}+11\beta_{3} q^{17}+\cdots\)
1152.4.f.d	$1152$	$4$	1152.f	24.f	$2$	$4$	$4$	$67.970$	\(\Q(\zeta_{8})\)	None		✓			1152.4.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta_{2} q^{5}+4\beta_1 q^{7}+8\beta_{3} q^{11}+\cdots\)
1152.4.f.e	$1152$	$4$	1152.f	24.f	$2$	$8$	$8$	$67.970$	8.0.\(\cdots\).8	None		✓			1152.4.f.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}-\beta _{2}q^{7}-\beta _{6}q^{11}+7\beta _{3}q^{13}+\cdots\)
1152.4.f.f	$1152$	$4$	1152.f	24.f	$2$	$12$	$12$	$67.970$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1152.4.f.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-3\beta _{4}-\beta _{6}+\cdots)q^{11}+\cdots\)
1152.4.f.g	$1152$	$4$	1152.f	24.f	$2$	$12$	$12$	$67.970$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1152.4.f.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{28}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-3\beta _{4}-\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1152, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)